We recently used lmer to analyze some reaction time data. There were three fixed effects variables, and the model included their interactions and a fully specified random effects structure. Something like
lm1 <- lmer(RT ~ A*B*C + (1+(A*B*C)|participant) + (1+(A*B*C)|item), data, REML = TRUE)
We found a three-way interaction, and interpreted it in a way that I thought was reasonable. However, a referee commented that, in order to interpret the coefficients associated with the interaction, we first has to compare nested models in order to ascertain the necessity of the different terms starting from the highest order interaction (and report the log likelihood Chi Square for the stats).
My understanding was that assessing nested models via likelihood ratio tests (to determine the best fitting model) and null hypothesis significance testing (e.g., to see if factor C has any effect) were separate issues. For example:
"LR tests can assess the significance of particular factors or, equivalently, choose the better of a pair of nested models, but some researchers have criticized model selection via such pairwise comparisons as an abuse of hypothesis testing..." from Bolker et al. (2008).
I know that something like lmerTest would do this kind of thing automatically, but I want to be sure I understand this. Does the referee comment make sense? Is this a disputed topic? Are there recommendations for further reading that I can do on this issue?